Bright yet dark: how strong coupling quenches exciton-polariton radiation

TL;DR

This paper develops a theoretical framework that reveals how strong exciton-photon coupling can suppress polariton radiation through destructive interference, enabling the creation of long-lived polaritonic states with potential applications in quantum technologies.

Contribution

It introduces a comprehensive model that surpasses the coupled oscillator approximation by capturing collective exciton-photon interactions and their impact on polariton radiative decay.

Findings

Strong coupling can suppress polariton radiation via destructive interference.

Polariton bound states in the continuum with infinite radiative lifetime are possible.

The model provides new design principles for long-lived polaritons.

Abstract

Understanding the radiative decay of exciton-polaritons is essential for achieving long-lived polaritons - a key prerequisite for enhancing nonlinear and quantum polaritonic effects. However, conventional wisdom - the coupled oscillator model - often oversimplifies polariton radiation as independent emissions from uncoupled excitonic and photonic resonances, overlooking the role of strong exciton-photon coupling in reshaping their radiative behavior. In this work, we present a theoretical framework that goes beyond the conventional coupled oscillator model by fully accounting for the collective and coherent nature of exciton-photon interactions. We demonstrate that these interactions can strongly suppress polariton radiation via destructive interference - both within the excitonic ensemble and between excitonic and photonic radiation channels - giving rise to polaritonic bound states in the continuum with infinitely long radiative lifetimes. Our approach offers a unified description of polariton radiative decay and establishes new design principles for engineering long-lived exciton-polaritons with tailored radiation properties, opening new avenues for nonlinear, topological, and quantum polaritonic applications.

Equations

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Full text

††preprint: APS/123-QED

Exciton-polaritons are hybrid quasiparticles formed through the strong coupling between excitonic resonances in solid-state materials and confined optical modes. Their dual light–matter nature gives rise to a rich landscape of physical phenomena and applications, ranging from polaritonic Bose–Einstein condensation [1] to polaritonic circuitry [2]. Recently, the integration of two-dimensional (2D) quantum materials, such as transition metal dichalcogenides (TMDs), into engineered nanophotonic structures has provided a new experimental platform for studying polariton physics, even at room temperature [3]. However, a fundamental challenge of polariton systems lies in the intrinsically short radiative lifetimes of polaritons, due to their open, dissipative nature: they can radiate into free space through both their excitonic and photonic components, leading to energy loss to the surrounding environment. This radiative decay is particularly pronounced for 2D exciton-polaritons, owing to their enhanced exciton oscillator strength [4]. As a result, their lifetimes are typically limited to $\sim$ 1 ps – shorter than the characteristic timescales for polariton interactions or thermalization – restricting access to many collective and nonlinear polaritonic phenomena. Overcoming this limitation and achieving longer polariton lifetimes remains a critical step toward advancing both fundamental research and practical applications of 2D polaritonic systems.

The radiative decay of exciton-polaritons is often modeled using the coupled oscillator model, which assumes that the excitonic and photonic components decay independently, each at its intrinsic rate [5, 6, 7, 8]. Despite its widespread use, this phenomenological approach fails to capture the dissipative nature of exciton-polariton systems - particularly how collective and coherent exciton-photon interactions influence their radiative behavior. For example, when an ensemble of non-interacting exciton resonances coherently couples to an optical mode, it forms a collective exciton state whose spatial profile mirrors that of the optical field. This profile can vary substantially, especially in nanophotonic structures with subwavelength features, such as photonic crystal (PhC) slabs [9]. As a result, radiation from the collective exciton state into free space is governed by interference among exciton emissions at different spatial locations, making it highly sensitive to their spatial distribution. Depending on the mode profiles, this interference can be strongly destructive, leading to significant suppression – or even complete quenching – of the collective exciton emission [10, 11, 12, 13]. This collective exciton behavior stands in sharp contrast to that of a bare material in a homogeneous dielectric environment, where excitons are uniformly excited during transmission or reflection measurements, resulting in in-phase radiation. Moreover, since polaritons are coherent superpositions of collective exciton and photon modes, their emission is governed by the interference between the excitonic and photonic radiation channels. This interference can, in certain cases, be completely destructive, leading to vanishing polariton radiative decay, even though neither the collective exciton nor the photon mode is individually dark. In contrast, the coupled oscillator model overlooks the detailed radiative mechanisms of the collective exciton and photon modes, and therefore fails to capture this interference-induced cancellation. Accurately modeling polariton radiative decay thus requires a more rigorous theoretical treatment that explicitly accounts for the collective and coherent nature of exciton-photon interactions.

Here, we develop a theoretical framework for exciton-polaritons in nanophotonic structures that goes beyond the coupled oscillator model. Within this framework, we show that polariton radiation can be dramatically suppressed through the engineering of nanophotonic structures, leading to the emergence of polaritonic bound states in the continuum (BICs) – exotic states that coexist with the radiation continuum without emitting energy [14]. Starting from a full Hamiltonian that captures the coupling between excitons, photons, and the radiation continuum, we identify two distinct mechanisms underlying the formation of polaritonic BICs. First, symmetry-protected polaritonic BICs arise at high-symmetry points in the photonic Brillouin zone (BZ), where both the collective exciton and photon modes are symmetry-incompatible with radiative modes, leading to suppressed far-field radiation. Second, polaritonic BICs can also emerge at arbitrary $k$-points in the BZ via complete destructive interference between the excitonic and photonic radiation channels. These polaritonic BICs, analogous to their photonic counterparts, exhibit vanishing radiative losses, with lifetimes limited solely by nonradiative exciton decay. Our theoretical predictions are supported by numerical simulations using realistic material parameters.

We begin by considering a MoSe2 monolayer placed on top of an InGaP photonic crystal slab patterned with a square lattice of air holes, as depicted in Fig. 1. The PhC slab supports an isolated, dispersive photonic band near the exciton resonance. In contrast, the exciton band exhibits negligible dispersion and remains flat across the entire photonic BZ. The Bloch Hamiltonian at momentum k, describing the TMD-PhC system and the radiation continuum, can be written as:

[TABLE]

Here $\omega_{\text{p}}$ and $\omega_{\text{x}}$ denote the photon and exciton mode frequencies, respectively. The operator $a_{\textbf{k}}^{\dagger}$ creates a PhC mode with crystal momentum k, while $b_{\textbf{k}^{\prime},\sigma}$ creates a plane-wave exciton mode with in-plane momentum $\textbf{k}^{\prime}=\textbf{k}+\textbf{G}_{mn}$, where $\textbf{G}_{mn}$ is the reciprocal lattice vector of the PhC labeled by integers $m$ and $n$. The index $\sigma\in{x,y}$ labels the two orthogonal in-plane polarizations of the exciton resonances. Note that, below the diffraction limit, only the exciton mode $b^{\dagger}_{\textbf{k},\sigma}$ exhibits far-field exciton emission. The operator $s^{\dagger}_{\omega,d}$ creates a free-space mode with in-plane momentum k and frequency $\omega$, where the index $d$ specifies both the polarizations (two orthogonal states) and the propagation direction (upward or downward). Owing to the strong periodic index modulation in the PhC, the electric field of the PhC mode at the monolayer plane consists of a superposition of plane waves with in-plane momenta $\textbf{k}^{\prime}=\textbf{k}+\textbf{G}_{mn}$ [15]. Consequently, the PhC mode $a^{\dagger}_{\textbf{k}}$ couples to all exciton modes $b^{\dagger}_{\textbf{k}^{\prime},\sigma}$ with coupling amplitudes $g_{\textbf{k}^{\prime},\sigma}$ determined by the corresponding plane-wave components of the photonic mode (see Supplemental Material). This is to be distinguished from exciton-photon coupling in photonic structures with continuous in-plane translation symmetry (e.g., distributed Bragg reflector cavities), where the optical field at the monolayer plane is simply a plane wave and couples only to the exciton mode with the same in-plane momentum k. The parameters $\kappa_{\omega,d}$ and $\gamma_{\omega,d,\sigma}$ quantify the coupling of the photonic $a_{\textbf{k}}^{\dagger}$ and excitonic $b_{\textbf{k},\sigma}^{\dagger}$ modes to the radiation continuum, respectively, and can be independently extracted from measurements of the bare material and the PhC slab.

One of the key distinctions between our framework and the conventional coupled oscillator model lies in how strong exciton-photon coupling modifies exciton emission. Specifically, the ensemble of exciton modes $b^{\dagger}_{\textbf{k}^{\prime},\sigma}$ interacts collectively with the photon mode $a^{\dagger}_{\textbf{k}}$ in a manner reminiscent of superradiance [16]: the exciton modes combine coherently to form a single collective (superradiant or bright) exciton mode $x_{\textbf{k}}^{\dagger}$, whose spatial profile mirrors that of the optical field at the monolayer plane. As a result, it couples to the optical mode with an enhanced strength $g=\sqrt{\sum_{\textbf{k}^{\prime},\sigma}|g_{\textbf{k}^{\prime},\sigma}|^{2}}$, forming upper (UP) and lower (LP) polariton states (see Supplemental Material). Importantly, the collective exciton emission, denoted $\beta_{\omega,d}$, can be strongly suppressed compared to that of the uncoupled exciton resonances ($\gamma_{\omega,d}$) due to the reduced weight of $b^{\dagger}_{\textbf{k},\sigma}$ in $x^{\dagger}_{\textbf{k}}$. As we will show later, this collective exciton emission can even vanish entirely when $x_{\textbf{k}}^{\dagger}$ contains no contribution from $b_{\textbf{k},\sigma}^{\dagger}$. In real space, this suppression reflects the spatially varying mode profile of $x_{\textbf{k}}^{\dagger}$ induced by the nanophotonic structure, where exciton emissions from different positions within a photonic unit cell interfere destructively. This highlights a fundamental limitation of the coupled oscillator model, which typically relies on the properties of uncoupled exciton resonances to analyze polariton radiation. In addition to this collective exciton mode, there exists a set of orthogonal, subradiant exciton modes that remain decoupled from the PhC mode and are thus neglected in the following analysis.

Another crucial feature of our formalism is the interference between photonic and excitonic emission channels – an effect neglected in the coupled oscillator model. To illustrate this, we rewrite the Hamiltonian in the polariton basis defined by $p^{\dagger}_{\textbf{k},\pm}=c_{\text{p}}a^{\dagger}_{\textbf{k}}\pm c_{\text{x}}x^{\dagger}_{\textbf{k}}$ , where $c_{\text{p}}$ and $c_{\text{x}}$ represent the photon and exciton fractions, respectively. In this basis, the Hamiltonian takes the form

[TABLE]

Here, $\omega_{\pm}$ denote the UP and LP frequencies. The coupling coefficients $\tau_{\omega,d,\pm}=c_{\text{p}}\kappa_{\omega,d}\pm c_{\text{x}}\beta_{\omega,d}$ characterize the interactions of the polariton modes $p^{\dagger}_{\textbf{k},\pm}$ with the radiation continuum. This highlights a key physical insight: polariton radiation arises from the coherent interference between the photonic and excitonic radiation channels, rather than from their simple weighted sum $|\tau_{\omega,d}|=|c_{\text{p}}\kappa_{\omega,d}|+|c_{\text{x}}\gamma_{\omega,d}|$, as is often assumed in the coupled oscillator model.

Using this theoretical framework, we demonstrate how collective and coherent exciton-photon interactions can fundamentally modify polariton radiation, resulting in polaritons with infinite radiative lifetimes. First, we show that both collective exciton and photon radiation can simultaneously vanish at high-symmetry points in momentum space due to symmetry constraints, leading to the emergence of symmetry-protected polaritonic BICs. Specifically, we consider a photonic band that is non-degenerate at the $\Gamma$ point. The corresponding photonic mode at $\Gamma$ is even under the in-plane two-fold rotation ($C_{2}^{z}$) operation, whereas the free-space radiation modes are odd. As a result, the photonic mode cannot couple to the radiation continuum and forms a symmetry-protected photonic BIC [14]. When a TMD monolayer is strongly coupled to this photonic mode, the resulting collective exciton mode inherits its symmetry. In contrast, the exciton mode $b_{\Gamma,\sigma}^{\dagger}$ is odd under $C_{2}^{z}$ and thus does not contribute to the collective exciton mode. Consequently, the collective exciton mode also becomes dark (i.e., $\beta_{\omega,d}=0$), giving rise to symmetry-protected polaritonic BICs at $\Gamma$.

To verify this, we calculate the momentum-resolved transmission spectra of the coupled TMD-PhC slab using finite-difference time-domain simulations [17]. The TMD monolayer is modeled as a Lorentz medium with finite nonradiative exciton decay [18, 19]. As shown in Fig. 2a, when the exciton energy ($E_{\text{x}}=$ 1.654 eV) is nearly resonant with the photonic BIC, strong exciton-photon hybridization occurs near the $\Gamma$ point, giving rise to upper and lower polariton branches. The observed Rabi splitting of 15 meV between the UP and LP branches at $\Gamma$ agrees well with experimental values reported in similar TMD–PhC systems [20], supporting the validity of our simulation. In addition to the polaritonic bands, a nearly flat exciton band emerges within the polariton gap, corresponding to subradiant exciton modes that remain decoupled from the PhC mode.

Remarkably, both LP and UP branches exhibit narrowing linewidths and diminishing Fano features as they approach $\Gamma$ and ultimately disappear – signifying the emergence of polaritonic BICs. To quantify the suppression of polariton radiation, we extract the radiative and total linewidths of the polariton modes by fitting the transmission spectra. As shown in Fig. 2c, the radiative linewidths (full-width at half-maximum) of both the LP and UP branches decrease monotonically as k approaches $\Gamma$, ultimately vanishing entirely. In contrast, their total linewidths saturate at half the nonradiative exciton linewidth ($\gamma_{\text{x},\text{nr}}=$0.8 meV), indicating that nonradiative exciton decay becomes the sole dissipation channel for polaritonic BICs. These narrow polariton linewidths stand in stark contrast to the predictions of the coupled oscillator model (purple line in Fig. 2c), where the polariton linewidths are given by the weighted sum of the bare exciton and photon linewidths. Furthermore, akin to their photonic counterparts, these polaritonic BICs have a topological origin, manifesting as polarization vortices centered at $\Gamma$ in the far-field radiation pattern (Fig. 2d) [21]. This topological character imparts robustness against structural perturbations that preserve $C_{2}^{z}$ symmetry.

In addition to those protected by symmetry, polaritonic BICs can also emerge at arbitrary momentum points where both the collective exciton and photon modes are bright ($\kappa_{\omega,d},\beta_{\omega,d}\neq 0$), yet their far-field emissions destructively interfere and perfectly cancel. To demonstrate this, we consider a TMD monolayer embedded at the central plane of the PhC slab, ensuring that the structure preserves up-down mirror symmetry ($\sigma_{z}$). The bare PhC band hosts an off-$\Gamma$ BIC at $k_{0}a/2\pi=$ 0.204, with energy aligned with that of bare excitons. As shown in Fig. 3a, strong exciton-photon hybridization near $k_{0}$ leads to the formation of upper and lower polariton branches, with a nearly flat bare exciton band residing within the polariton gap. Remarkably, polaritonic BICs emerge in both the UP and LP branches, with their positions symmetrically displaced on either side of $k_{0}$. Fig. 3b,c show the polarization distributions of the far-field radiation patterns for the UP and LP branches, respectively, confirming the presence of polarization vortices at the BIC locations. The emergence of these polaritonic BICs marks a significant deviation from the coupled oscillator model, which predicts finite polariton radiation near $k_{0}$ due to non-vanishing exciton and photon emissions.

The origin of these off-$\Gamma$ polaritonic BICs can be attributed to interference effects. Along the $\Gamma\text{X}$ direction, the radiation amplitudes of both the exciton and photon components are generally complex functions of $k_{x}$. However, the presence of $\sigma_{z}$ symmetry allows both amplitudes to be made real under an appropriate gauge choice. In the vicinity of the photonic BIC at $k_{0}$, the photonic radiation amplitude $\kappa_{\omega,d}$ undergoes a sign flip, while the excitonic radiation $\beta_{\omega,d}$ remains approximately constant. This allows tuning of $k_{x}$ such that the exciton and photon radiation amplitudes exactly cancel ($c_{\text{p}}\kappa_{\omega,d}\pm c_{\text{x}}\beta_{\omega,d}=0$), leading to the formation of a polaritonic BIC at a momentum point near $k_{0}$. Moreover, the relative phase between the collective exciton and photon modes differs by $\pi$ in the UP and LP branches, causing the polaritonic BICs to occur on opposite sides of $k_{0}$.

To further confirm the interference-based mechanism, we show that perfect destructive interference breaks down when the up-down mirror symmetry is broken. To this end, we simulate the transmission spectrum of a structure where the TMD monolayer is slightly lifted from the central plane of the PhC by 20 nm. As shown in Fig. 4a, both the upper and lower polaritonic BICs vanish simultaneously, and the polariton band linewidths remain finite near $k_{0}$. This behavior arises because both the collective exciton and photon radiation amplitudes become generically complex, making tuning $k_{x}$ alone insufficient to achieve perfect destructive interference. This can also be understood from a topological perspective: as shown in Fig. 4b, breaking $\sigma_{z}$ causes the integer polarization vortex – originally pinned to the $k_{x}$-axis and associated with vanishing far-field radiation – to split into a pair of half-integer vortices with the same winding number and finite far-field radiation, displaced symmetrically about the $k_{x}-$axis. A similar phenomenon has been observed in dielectric photonic crystals with broken up-down mirror symmetry [22].

In summary, we present a theoretical framework for investigating the radiative decay of exciton-polaritons in nanophotonic structures that goes beyond the conventional coupled oscillator model. We demonstrate that the collective and coherent nature of exciton-photon interactions can dramatically modify polariton radiation, particularly in nanophotonic environments with spatially varying optical fields, enabling the formation of polaritonic BICs with theoretically infinite radiative lifetimes. While our analysis focuses on the coupling between a TMD monolayer and a PhC slab, the underlying principles are broadly applicable to a wide range of material systems – such as III-V quantum wells [5] and perovskites – and various photonic platforms, including PhC nanocavities [20] and plasmonic structures [23]. Our work paves the way for realizing exciton-polaritons with ultra-long lifetimes, offering promising prospects for both classical and quantum polaritonic applications, including low-threshold nonlinear polaritonics [20], topological polaritonics [9], and quantum polaritonic phenomena [24, 25].

Author Contributions

L.H. and B.Z. conceived the idea. J.S. and L.H. developed the theory and performed the numerical simulations. All authors discussed the results and wrote the paper.

Acknowledgements.

This work was partly supported by the U.S. Office of Naval Research (ONR) through grant N00014-20-1-2325 on Robust Photonic Materials with High-Order Topological Protection and grant N00014-21-1-2703, as well as the Sloan Foundation. L.H. acknowledges support from the MonArk NSF Quantum Foundry supported by the National Science Foundation Q-AMASE-i program under NSF Award No. DMR-1906383.